Story highlights

The foreign ministers say Iran is inciting unrest with its "hostile and provocative statements"

Protesters angry about a Shiite cleric's execution stormed the Saudi embassy in Tehran last weekend

Members of the Gulf Cooperation Council meet in Riyadh, agree to call embassy attack terrorism

Riyadh, Saudi Arabia (CNN)A six-nation Middle Eastern alliance agreed Saturday to characterize the recent attack on Saudi Arabia's embassy in Tehran as an act of terror -- strong language that marks an even further escalation in a tiff that has embroiled the region for days.

Foreign ministers from the six Gulf Cooperation Council met in the Saudi Arabian capital of Riyadh, after which alliance Secretary-General Abdul Latif Zayani read a statement indicating that the nations agreed to label last weekend's incident as terrorism.

Zayani himself a few days ago referred to the Saudi Embassy as a terrorist act, so this terminology isn't entirely new. Still, it is significant in that the six GCC countries -- Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates -- are now officially on the same page.

It also suggests countries in the region aren't acceding to requests from the United Nations, United States and other officials to tone down their rhetoric and refocus on other issues, like peacefully ending Syria's civil war and dealing with ISIS.

Iranian protesters hold portraits of prominent Shiite Muslim cleric Nimr al-Nimr as they confront riot police during a demonstration against his execution by Saudi authorities on Sunday, January 3, outside the Saudi embassy in Tehran, Iran. Saudi Foreign Minister Adel al-Jubeir told reporters that Saudi Arabia is severing ties with Iran after an attack on the embassy.

Iranian demonstrators burn representations of the U.S. and Israeli flags during a demonstration in front of the Saudi Arabian Embassy in Tehran on January 3.

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Photos:Protest in Tehran after Saudis execute cleric

Iranian security guards Saudi Arabia's embassy in Tehran while a group of demonstrators gathered to protest on January 3.

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Photos:Protest in Tehran after Saudis execute cleric

Protesters set fire to the Saudi Embassy in Tehran, Iran, on Saturday, January 2, during a demonstration against the execution of prominent Shiite Muslim cleric Nimr al-Nimr by Saudi authorities. Nimr was a driving force of the protests that broke out in 2011 in Saudi Arabia's east, an oil-rich region where the Shiite minority of an estimated 2 million people complains of marginalization.

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Photos:Protest in Tehran after Saudis execute cleric

Smoke billows from the windows of the burning Saudi Embassy on January 2. A CNN producer in Tehran said some protesters made it inside the building, setting fire and ransacking some records.

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Photos:Protest in Tehran after Saudis execute cleric

A firefighter sprays water on the flames on January 2 in Tehran, Iran, a Shiite-majority nation, issued a statement deploring the execution and warning that Saudi Arabia would pay a heavy price for its policies.

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Photos:Protest in Tehran after Saudis execute cleric

Iranian protesters gather outside the Saudi Embassy in Tehranon January 2. Saudi Arabia said it executed "terrorists" and told Iran to stay out of its internal affairs.

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Photos:Protest in Tehran after Saudis execute cleric

Several protesters were arrested, police officers at the embassy told CNN.

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Photos:Protest in Tehran after Saudis execute cleric

There was some damage near the back of the embassy building, witnesses and a police officer said. None of the Saudi diplomatic staff was in the embassy at the time.

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That attack spurred Saudi Arabia to sever official ties with Iran, its longtime regional rival. Several other countries -- most of them led by and/or containing mostly Sunni Muslims, like Saudi Arabia, as opposed to Shiite-led Iran -- joined in. In that respect, this spat continues the schism that happened 14 centuries ago when Sunnis and Shiites split over who should succeed the Prophet Mohammed as Islam's leader.

"Of course, the Saudi government, in order to cover up its crime of beheading a religious leader, has resorted to a strange measure and has severed its ties with the Islamic Republic," Rouhani said, according to Iran's state-run Press TV. "Undoubtedly, such moves will never hide that great crime."

Ministers accuse Iran of 'direct incitements'

The Gulf ministers who met Saturday in Riyadh, though, together insisted that Iran is in the wrong -- not just because of the embassy attacks specifically, but due to its actions and comments criticizing the Saudi executions.

That report called "Iranian hostile and provocative statement on the judicial rulings implements (in Saudi Arabia) against a number of terrorists" as "direct incitements for launching attacks on the diplomatic missions."

The same council also raised other gripes against Tehran, like its "continued occupation of ... three United Arab Emirates islands, ... spread of sectarian strife, support for terrorist organizations and incitement to undermine security and stability in GCC countries."

The SPA report concluded, "The GCC Ministerial Council urged the international community to take necessary measures to compel Iran to respect the principle of good neighborliness, to stop its activities destabilizing the region, to stop its support for terrorism, to not interfere in the internal affairs of the GCC countries and the region's countries, and to not use or threaten to use force."

CNN's Nic Robertson reported from Riyadh, and CNN's Greg Botelho reported and wrote from Atlanta. CNN's Jon Jensen contributed to this report.